Question

Greta Thunberg, a 16-year-old climate activist, led a global climate strike on Friday September 20, 2019 to protest government and business inaction on climate change. A recent Gallup poll showed that 47% of Americans said they worry a great deal about the quality of the environment and the impacts of climate change. Assume that 47% holds for the population of U.S. adults and suppose that a survey of a random sample of 50 U.S. adults is conducted in which they are asked whether or not they are concerned about climate change. Let X represent the number of these 50 who report they are concerned about climate change. Then X is a binomial random variable.

1. Identify the number of trials n and the probability of success p for this binomial experiment.

2. what is the probability that exactly 30 of those surveyed are concerned about climate change? Label your answer with appropriate probability notation.

3.Write out the formula (with the appropriate values substituted) for finding the probability that exactly 30 of those surveyed are worried about climate change.

4. Compute the mean number of U.S. adults who are concerned about climate change in a random sample of 50 U.S. adults. Label your answer with the appropriate symbol

5. Compute the standard deviation of the number of U.S. adults who are concerned about climate change in a random sample of 50 U.S. adults. Round your final answer to two decimal places. Label your answer with the appropriate symbol

6. According to the Empirical Rule, within what range of values will approximately 95% of the observations in this binomial experiment fall?

7. Would it be unusual to find only 12 U.S. adults who are concerned about climate change in a random sample of 50 U.S. adults? Why?

Answer 1

Here, all probabilities are calculated using binomial distribution calculator.